Hydrodynamic Mechanics of Wave-Particle Duality and the Kinematic Derivation of Fermionic Spin

This paper provides a deterministic, local mechanical framework for two of the most elusive phenomena in the microcosm: wave-particle duality and fermionic spin-½ . Under the framework of Quantum Continuum Mechanics, we demonstrate that the probabilistic formalism of the wave function can be physically understood as the real tensional perturbation of a pilot wave propagating through a viscoelastic background termed the Closed String Matrix (CSM). By defining the free electron as an autonomous micro-vortex, the double-slit experiment is resolved via deterministic hydrodynamic guiding. Furthermore, the 720° rotation paradox of fermions is modeled as a three-dimensional elastic holonomy, allowing us to derive the Dirac Equation kinematically as the Navier-Stokes equivalent for shear stress within a continuous medium. Low-energy experimental forecasts are provided.